Adaptive filtering for stochastic risk premia in bond market

We consider the adaptive filtering problem for estimating the randomly changing risk premium and its system parameters for zero-coupon bond models. The term structure model for a zero-coupon bond is formulated including the stochastic risk-premium factor. We specify our observation data from the yield curve and bond data which are used to hedge some option claims. For the xed system parameters, the Kalman filter for the risk-premium and the factor process is constructed first. Secondly, by using the parallel filtering technique and resampling technique commonly used in particle filters, the on-line estimation algorithm for model parameters is constructed. Some simulation studies are nally presented

Identification of affine term structures from yield curve data

We consider a slight perturbation of the Hull-White short rate model and the resulting modified forward rate equation. We identify the model coefficients by using the martingale property of the normalized bond price. The forward rate and the system parameters are then estimated by using the maximum likelihood method

Silting mutation in triangulated categories

In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'. In this paper we focus on `tilting mutation', which has a disadvantage that it is often impossible, i.e. some of summands of a tilting object can not be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing `silting mutation' for silting objects as a generalization of `tilting mutation'. We shall develope a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with `silting mutation' by generalizing the theory of Riedtmann-Schofield and Happel-Unger. We show that iterated silting mutation act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally we give a bijection between silting subcategories and certain t-structures.Comment: 29 page

Infinite dimensional parameter identification for stochastic parabolic systems

The infinite dimensional parameter estimation for stochastic heat diffusion equations is considered using the method of sieves. The consistency property is also studied for the long run data

The co-stability manifold of a triangulated category

Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied intensively. However, there are mainstream triangulated categories whose stability manifold is the empty set. One example is the compact derived category of the dual numbers over an algebraically closed field. This is one of the motivations in this paper for introducing co-stability conditions as a 'continuous' generalisation of co-t-structures. Our main result is that the set of nice co-stability conditions on a triangulated category is a manifold. In particular, we show that the co-stability manifold of the compact derived category of the dual numbers is the complex numbers.Comment: 14 page

Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles

Glacial-interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is $\sim$40 kyr before the so-called middle Pleistocene transition between $\sim$1.2 and $\sim$0.7 Myr ago, and it is $\sim$100 kyr after the transition. In this paper, the dynamics of glacial-interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.Comment: 25 pages, 9 figure